After wondering the same thing myself for sometime, having read several
books that dealt in part with this issue, and thinking it over myself;
I've come to my own personal conclusions:

 * 3,000,000 player pianos were built between 1907 and 2001.
 * 125,000 of these were expression pianos.
 * 400,000 players remain, whether they work or not.  Most do not work.
 * 80,000 work pretty well, and there are still 7,000 working
   expression pianos.
 * There are 10,000,000 pianos in the United States; working or
   not working, from recreation room spinets to concert grands.

So, 1 in 25 pianos is a player piano.  1 in 125 pianos is a working
player piano.  1 in 1400 pianos is a working expression piano.

I'm almost certain that they are far more common in certain parts of
the country.  The New York/Philadelphia metroplex is a major focus of
the instruments since many of them were made here, as were the rolls!

I'm sure that most of rest of them are to be found along the remainder
of the Eastern Seaboard, in the Chicago/Detroit/Cleveland area, and in
and around San Francisco, Seattle, and Portland.

I think my estimate is fairly reasonable and "within the ballpark."

Sincerely,

Gabe Della Fave